The whole question is whether Longstreet is sent west Before or After Chancellorsville.
If before...
Lee would have convinced Davis that the troops already guarding Richmond could have faced off Burnside and the 9th corps on the Peninsula (really happened, the Confederates defended well enough), and that Longstreet would be able to actually do something in the west.
Longstreet would need to take some of his troops with him, probably, as in real life, he would take Pickett and Hood, maybe another division (McLaws, Anderson, etc), meaning a sum force of somewhat more than 20,000 men, leaving Lee along the Rapahannock with ~50,000, and Jackson as main subordinate. So, there would be no significant change in the east until at least after Chancellorsville.
By the time Longstreet got west, Grant would have just about surrounded Vicksburg. So, it follows that Longstreet would combine with Johnson, resulting in an actually substantial relief force of about 40,000 men, who could reach the area by early June, or, early enough.
To keep things interesting, let's say that Johnson is wounded (again) during preliminary skirmishing, and that Longstreet assumes command, and after a historic fight near the southern defenses, breaks Grant's line. Grant retires a short distance to the north, but the combined force of Longstreet and Pemberton is about 50-60,000, or, almost as much as Grant. This would blunt the drive on Vicksburg for a time, and Grant, while not being recalled, would suffer a blow to his reputation. Surely Halleck or Lincoln would order him back north, or even east, to Tullahome, just in time for Rosecrans' drive.........
If after...
Jackson has been killed, so Longstreet is Lee's main subordinate and a very trusty one. The only possible reason for him to be sent west is to make a big difference. This means either destroying Rosecrans or relieving Pemberton. In any case, Lee's reunited army actually grows at first, reaching the 70,000 men it had for the Gettysburg Campaign in real time.
Davis trusted Bragg many times over, so he would expect that Bragg needed no help. Longstreet would therefore go to Vicksburg, with a substantial force (Hood, McLaws, Pickett, and some detached brigades). In fact, he would be sent to relieve Johnson, who was promoted to overall commander in the west. A similar scenario to the above happens, only one month later.
Meanwhile, Lee has 40-50 thousand men, which is actually quite enough, due to the expiring 2-year enlistments in the AotP (real), leaving it with 80-90 thousand men and a disgraced leader. Lee would re-divide his army, appoint one wing to A. P. Hill, and the other to R. S. Ewell, as in real time. They would have about the same composition as before, EXCEPT...
with Richmond secure (thanks to earlier real-time efforts by Longstreet), D. H. Hill and another division from the south would arrive near Fredericksburg. They would be placed directly under Lee's command.
His grand plan for destroying Hooker's army (Hooker was kept, because there was no Gettysburg Invasion yet, so no crisis):
A. P. Hill takes his own division, which is quite large, Anderson's, Colston's/whoever took over from Jackson, and some cavalry to the Shenandoah Valley, go north towards Washington, as a diversion to take Hooker away from the Rapidan (it's 2nd Bull Run campaign, but new people). Meanwhile, Lee, commanding D. H. Hill, the other commander, and Ewell's corps, consisting of his own division, Early's, Rhodes', and there's one left over that I am fogetting), directly north, following Hooker on the retreat (he calls it 'repositioning). Meanwhile, Lee also freed JEB Stuart to go galavanting off in the area behind Hooker and stir up whatever trouble he can. He goes for a counter-clockwise circling of the whole Union army, only this time, he succeeds. Lee's three mentioned wings finally meet, and engage Hooker's forces just west of the Bull Run Creek, on eerily familiar ground.........
Feel free to point out any significant problems with these scenarios

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